Related papers: Spherical Manifold in Quantum Evolution
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant…
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $\phi(k,E)$ is…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
The determination of the quantum state of a single system by protective observation is used to justify operationally a formulation of quantum theory on the quantum state space (projective Hilbert space) $\cal P$. Protective observation is…
The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…